1570af302Sopenharmony_ci#include "libm.h" 2570af302Sopenharmony_ci 3570af302Sopenharmony_ci/* asinh(x) = sign(x)*log(|x|+sqrt(x*x+1)) ~= x - x^3/6 + o(x^5) */ 4570af302Sopenharmony_cidouble asinh(double x) 5570af302Sopenharmony_ci{ 6570af302Sopenharmony_ci union {double f; uint64_t i;} u = {.f = x}; 7570af302Sopenharmony_ci unsigned e = u.i >> 52 & 0x7ff; 8570af302Sopenharmony_ci unsigned s = u.i >> 63; 9570af302Sopenharmony_ci 10570af302Sopenharmony_ci /* |x| */ 11570af302Sopenharmony_ci u.i &= (uint64_t)-1/2; 12570af302Sopenharmony_ci x = u.f; 13570af302Sopenharmony_ci 14570af302Sopenharmony_ci if (e >= 0x3ff + 26) { 15570af302Sopenharmony_ci /* |x| >= 0x1p26 or inf or nan */ 16570af302Sopenharmony_ci x = log(x) + 0.693147180559945309417232121458176568; 17570af302Sopenharmony_ci } else if (e >= 0x3ff + 1) { 18570af302Sopenharmony_ci /* |x| >= 2 */ 19570af302Sopenharmony_ci x = log(2*x + 1/(sqrt(x*x+1)+x)); 20570af302Sopenharmony_ci } else if (e >= 0x3ff - 26) { 21570af302Sopenharmony_ci /* |x| >= 0x1p-26, up to 1.6ulp error in [0.125,0.5] */ 22570af302Sopenharmony_ci x = log1p(x + x*x/(sqrt(x*x+1)+1)); 23570af302Sopenharmony_ci } else { 24570af302Sopenharmony_ci /* |x| < 0x1p-26, raise inexact if x != 0 */ 25570af302Sopenharmony_ci FORCE_EVAL(x + 0x1p120f); 26570af302Sopenharmony_ci } 27570af302Sopenharmony_ci return s ? -x : x; 28570af302Sopenharmony_ci} 29